Results 21 to 30 of about 213 (131)
Subcritical Turing bifurcation and the morphogenesis of localized patterns
Physical Review E, 2014 6 pages, 4 ...
Breña-Medina, Víctor, Champneys, Alan
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A graph-theoretic method for detecting potential Turing bifurcations [PDF]
The Journal of Chemical Physics, 2006 The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical ...
Mincheva, Maya, Roussel, Marc R.
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Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model
Discrete Dynamics in Nature and Society, 2019 In this paper, a discrete predator-prey system with the periodic boundary conditions will be considered. First, we get the conditions for producing Turing instability of the discrete predator-prey system according to the linear stability analysis.
Lili Meng +3 more
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Turing-Hopf patterns in a morphochemical model for electrodeposition with cross-diffusion
Applications in Engineering Science, 2021 This paper focuses on the impact of cross-diffusion for Turing-Hopf instability in a morphochemical model for electrodeposition (DIB) and completes the analysis on the role of cross-diffusion on pattern formation in electrodeposition we recently carried ...
Deborah Lacitignola +2 more
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Additive Global Noise Delays Turing Bifurcations
Physical Review Letters, 2007 We apply a stochastic center manifold method to the calculation of noise-induced phase transitions in the stochastic Swift-Hohenberg equation. This analysis is applied to the reduced mode equations that result from Fourier decomposition of the field variable and of the temporal noise. The method shows a pitchfork bifurcation at lower perturbation order,
Hutt, Axel +2 more
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Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay
Complexity, 2020 In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model.
Feifan Zhang +4 more
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Convective Turing bifurcation with conservation laws
, 2023 Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model reaction-diffusion and reaction-convection-diffusion equations, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation in the presence of conservation laws. In the nonconvective, reaction-diffusion case, this is seen similarly as in \
Wheeler, Aric, Zumbrun, Kevin
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Studies on the Existence of Unstable Oscillatory Patterns Bifurcating from Hopf Bifurcations in a Turing Model [PDF]
Journal of Applied Mathematics, 2014 We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain. With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of proving the existence of Hopf bifurcations, which suggests the existence of spatially homogeneous and ...
Yan Zhang, Zhenhua Bao
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Boundary Value Problems, 2019 In this paper, Turing patterns and steady state bifurcation of a diffusive Beddington–DeAngelis-type predator–prey model with density-dependent death rate for the predator are considered.
Hongwu Xu, Shengmao Fu
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Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense
Mathematics, 2020 In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered.
Maria Francesca Carfora +1 more
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